The invention relates to a flexible, tubular metal device e.g. a bellows with an internal diameter up to 60 millimeters, said device comprising one or more corrugated convolutions, said convolutions having an overall bell-like shape with rounded top portions and rounded bottom portions, where the curvature of the outside surface of the convolutions is numerically smaller at the top portions than at the bottom portions, said curvature being derived from a curve defined as the intersection of the outside surface of the device and a plane through the longitudinal axis of the device, and where the curvature of said curve changes sign only once at a change position located between a top portion and an adjacent bottom portion, and where the length of a first section on the curve is at least 10% longer than the length of a second section on the curve, said first section extending from one change position to an adjacent change position via a top portion, and said second section extending from one change position to an adjacent change position via a bottom portion.
Flexible, tubular devices such as bellows with one or more convolutions impart a degree of flexibility in pipelines carrying gas, air, water, steam, petrochemicals or any other substance at varying temperatures and pressures. Turbines, pumps, compressors, heat exchangers, reactors and valves are typical types of equipment where bellows can be used to absorb relative movements between the equipment and the connecting pipelines. Unless some compensation for these dimensional changes is provided, high stresses will be induced in the equipment or the piping and might lead to system failure. The inherent flexibility enables bellows to absorb movements in more than one direction and, thereby, leaves a greater degree of freedom in designing the layout of the piping system, compared to using conventional devices such as bends and loops.
In general, a bellows can be applied to four basic movement modes (or a combination of these): axial, angular, lateral, and torsional. The torsional mode is, however, often unwanted because it destabilises the convolution in a way that reduces its ability to absorb other modes. The bellow durability depends greatly on the geometry, the material properties, the manufacturing processes during production, and the boundary and load conditions, e.g. an unrestrained pressurised bellow will expand longitudinally, whereas an axially constrained bellow will restrain pressure thrust from the system without changing its dimensional length. The lifetime of each convolution depends, therefore, on a variety of factors but, in particular, on the ability to absorb movements while having geometry that avoids local peak loads.
The convolution geometry is often based on sound engineering principles and years of experience. This know-how is then used to design a bellows that may be required to withstand exposure to large variations in ambient temperature and pressure, e.g. during equipment start-up, one-time stretching under assembly or numerous movements when in operation. Designing a bellows for a piping system often requires, therefore, a thorough system response examination in order to avoid unfavourable conditions that can later lead to bellow failure.
Within the industry, it is commonly accepted that the leading cause of failure for bellows is due to fatigue or one-time damage during installation. In both cases the bellow is stressed beyond a characteristic threshold value, which leads to failure. A way to resolve this failure type, and thereby increase product liability, is to reduce the stresses during deformation by providing improved convolution geometry. The bellow geometry depends on the number of convolutions, as well as on the total length, skirt length, wall thickness and inner diameter. The convolution geometry depends on convolution height, pitch and wall thickness. These are the common design variables, which can be adjusted for a specific application through empirically based safety factors and years of experience. Often the design is based on modifications of a “U” span, “S” span, “V” span, or “Ω” span, from where engineering design data and safety factors are generated. These shapes are “built-up” from simple geometric shapes (primitives) like straight lines and circle sectors, which are easy to draw, analyse and easily programmable into a CNC interface before cutting metal for the forming tools. When such a convolution shape, combined with a material, which is often stainless steel, and a manufacturing process, fulfils customer requirements and expectations, the design may become the best practise within a specific area, even without being the best solution.
The susceptibility of the convolution to fatigue failure is, therefore, increased by geometric stress raisers that are more predominant than wall thickness variations such as material thinning in the convolution nose-tip area as a result of the forming process. For this reason, the bellow failure modes have resulted in the production of bellows in expensive high-grade materials, e.g. stainless steel, which allow a poor convolution design to offer an acceptable performance durability.
A bellow may be required to withstand a very large number of load cycles, such as those from a running engine. The cyclic stress range controls the overall fatigue life of the bellow and if the engine goes through several start-up and shut-down phases, the stress range will control the cumulative fatigue life. In both cases the fatigue life depends on the total number of completed cycles and upon the mean stress and total stress range to which the bellow is subjected. With a decreased amount of stress, a bellows will withstand a greatly increased number of repetitions before failure, whereas at a higher stress level, failure will occur after a relatively fewer number of reversals.
When bellows need to be specially designed for a high cyclic life, the literature is scarce in specifying characteristic design variables or dimensional ranges for an optimal convolution shape. In these cases, the bellow manufacturer must be advised of the expected number of cycles and, based on empirical generated design data from historical successful designs in connection with estimated material and manufacturing constants, a safe convolution design might emerge. The literature is, in addition, limited with regard to estimating fatigue data for calculating the lifetime of current standard spans, e.g. the data varies greatly when the pitch-height convolution ratio varies.
Guidance on design of bellows etc. may e.g. be found in “Standards of the Expansion Joint Manufacturers Association, Inc.”, 25 North Broadway, Tarrytown, N.Y. 10591.
U.S. Pat. No. 6,006,788 discloses a metal tube having helical corrugations. The helical design is used for continuously winding a wire around the tube. The helical corrugations cause twisting of the tube when the tube is subjected to bending. In many automotive applications, fuel lines, brake lines etc. the ends of tubes/pipes are fixed, but vibrations and other movements will create repeated bending and thereby twist. However, the twist is locked due to the fixed ends whereby significant stresses are caused. Repeated stresses lead to metal fatigue and component failure.
The shape of the corrugations, as displayed in FIG. 4 of U.S. Pat. No. 6,006,788, is a combination of smaller circular sections with radius r and larger circular sections with radius R. Calculations have, however, shown that significant stress-raisers are present fx by the transitions between the circular sections. Although the disclosed shape may obtain high flexibility, the stress-raisers will decrease the live span under repeated loading due to fatigue. An improved design is hence desirable.